\documentclass[english]{rug08pres}

\usepackage[utf8]{inputenc}
\usepackage{default}

\begin{document}

\facname{Faculty of Mathematics\\ and Natural Sciences}
\group{Multi-Agent Systems}
\titleslide {What's My Number?}
C. Lier and Michiel van der Ree \\ \today

\slide[What's My Number: The Game]
\begin{itemize}
  \item So-called \textit{Headband deduction game}
  \item Nine numbered cards
  \item Three players, two cards each
  \item Twenty questions
    \begin{itemize}
      \item E.g. ``Do you see three consecutive numbers?''
    \end{itemize}
  \item Inspired by \textit{Code 777} \ldots
  \item \ldots which was in turn inspired by \textit{What's That on My Head}
    (1963)
\end{itemize}

\slide[]
\vspace{10mm}
\begin{tabular}{c l}
  \parbox{0.7\textwidth}{
    \vspace{10 mm}
    \textit{WToMH}-creator Richard Abbott:\\\\
    \textit{Playing this game is not simply learning a logic system and then using
      it to process the information you receive. It's a lot more difficult -- and a
      lot more creative. You must develop your own logic system and then use it
      to process the information you receive.
    }
  }
  &
  \raisebox{\dimexpr\ht\strutbox-\height\relax}{\includegraphics[width=0.3\textwidth]{img/wtomh6.jpg}}
  \\
  \hline
\end{tabular}

\slide[Sources of information]
\begin{itemize}
  \item Two sources of information:
    \begin{enumerate}
      \item Answers to questions
e     \item The fact that no one knows her cards
    \end{enumerate}
  \item Compare games in which only the first source is used to games in which
    both sources are used
  \item Use one Kripke model to model players' knowledge
  \item $S$ consists of all possible card distributions
    \begin{itemize}
      \item 7560 in total
    \end{itemize}
\end{itemize}

\slide[The epistemic step]
\begin{itemize}
  \item Muddy children-esque twist 
 \item Given that nobody knows their cards yet, remove all accessibility
   relations to and from states in which at least one player would have known
   her cards.
 \item At the end of turn, do this once or \ldots
 \item \ldots do it until the model does not change any more
\end{itemize}

%\slide[Options]
%\begin{itemize}
% \item Epistemagic
% \subitem Once per turn
% \subitem Infinite
% \item Kooi's Choice
% \subitem Only true state possibilities
% \subitem Full model possibilities
%\end{itemize}

\slide[Kooi's Choice]
\begin{itemize}
 \item Player chooses the question
 \item True state/Full model
\end{itemize}

\slide[Experiments]
\begin{itemize}
 \item Simple vs. Epis
\end{itemize}

\slide[Results]

\slide[]
\vspace{10mm}
\begin{tabular}{c l}
  \parbox{0.7\textwidth}{
    \centering
    \vspace{20mm}
    \huge
    Questions?
    \vspace{20mm}
  }
  &
  \raisebox{\dimexpr\ht\strutbox-\height\relax}{\includegraphics[width=0.3\textwidth]{img/wtomh6.jpg}}
  \\
  \hline
\end{tabular}
\slide[Thank you!]

\end{document}
